Cosmic Everything Charts Compared

Standard ideas about gravity need to be questioned for many reasons. The most important reason is the gap in our empirical knowledge of gravity for the insides of material bodies. This gap could be filled in by doing a simple laboratory experiment. In the course of expounding on many of the other reasons, this essay often refers to a pair of charts that plot the mass, radius, density and acceleration of the whole range of objects in the physical universe on logarithmic scales. The Standard version is bound by an "edge of the world" corresponding to the alleged horizon of black holes. The other version, based on the Space Generation Model of gravity and cosmology (SGM), differs in that the black hole candidates are placed beyond (within) the horizon because in this model there are no black holes. Subjects covered include the dimensionality of space and the possibility that understanding gravity requires four, instead of three spatial dimensions. Current work on quantum gravity (much of which also appeals to hyper-dimensional space) is compared with the SGM. Cosmological implications are also discussed in detail. 90 references; 19 Figures.

Standard ideas about gravity need to be questioned for many reasons. The most important reason is the gap in our empirical knowledge of gravity for the insides of material bodies. This gap could be filled in by doing a simple laboratory experiment. In the course of expounding on many of the other reasons, this essay often refers to a pair of charts that plot the mass, radius, density and acceleration of the whole range of objects in the physical universe on logarithmic scales. The Standard version is bound by an "edge of the world" corresponding to the alleged horizon of black holes. The other version, based on the Space Generation Model of gravity and cosmology (SGM), differs in that the black hole candidates are placed beyond (within) the horizon because in this model there are no black holes. Subjects covered include the dimensionality of space and the possibility that understanding gravity requires four, instead of three spatial dimensions. Current work on quantum gravity (much of which also appeals to hyper-dimensional space) is compared with the SGM. Cosmological implications are also discussed in detail. 90 references; 19 Figures.

—Using logarithmic scales, it is possible to compactly show on a graph how the massesand sizes of all known physical objects in the universe relate to one another. Suchgraphs are necessarily skeletal. By ﬁlling in more detail than usual (e.g., Kraus, [1]Barrow, [2] and Hartle [3])and by adding density and gravitational acceleration tothe axes, the meaningfulness of these relationships becomes more strikingly per-ceptible. Organization of the ﬁrst chart (Figure 1) is entirely consistent with thestandard paradigm, with data obtained from the standard literature. The secondchart (Figure 2) is organized the same way. It uses the same data for mass, but itdiﬀers in that nine objects are placed

inside

the Schwarzschild horizon line, whichthereby reﬂects the absence of black hole horizons and singularities. A new modelof gravity, the Space Generation Model, is presented in support of the second chart.Most importantly, a relatively simple laboratory experiment is proposed whose re-sult would decisively refute either general relativity or the new model, and therebyindicate which chart is closer to the truth.PACS 04.80.Cc – Experimental tests of gravitational theories.

1. – Introduction

One of the most well known predictions of Einstein’s theory of gravity, general rela-tivity (GR) is that suﬃciently large and compact bodies of matter form

black holes

. Agraph that plots mass vs.radius on logarithmic scales so as to include a wide range of masses and sizes, shows such bodies lying on a straight line—as seen for nine points inFigure 1 (Chart 1). Figure 2 (Chart 2) is essentially the same graph except that thesenine points have been moved to the left of the black hole line. This essay concerns thereasons why the latter placement of these points makes more sense, which is tantamountto proposing a new model of gravity.For reasons that will be explained in detail, I call this the Space Generation Modelof gravitation and cosmology (SGM). A simple laboratory experiment would be the bestway to decide between GR and the SGM. The diﬀerence in predictions is not subtle;

c

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Richard Benish 2010

1

2

R. BENISH

it is dramatic. Even the weak ﬁeld regime of Newton’s theory of gravity is challenged.The SGM is thus radical in many ways. Yet it is consistent with all physical factsthat I know of. In what follows the SGM’s prediction for the proposed experiment willbe supported 1) by a critical assessment of not only GR, but of various foundationalconcepts of physics and 2) by showing that certain alternative concepts are logicallymore coherent. By developing these new concepts we will see that some of the persistentenigmas of contemporary physics disappear. We will venture far and deep and wide. Weseek to discover whether Chart 1 or Chart 2 serves as a better map of the world.Therefore, we’ll begin by pointing out a few general features of the charts. (Notethat, to facilitate printing or viewing at a larger size, they are available as stand-alonedocuments. [4,5]) The charts may be thought of as “globes” that allow the whole worldto be seen at a glance, rather than having to mentally piece it together with scattered bitsof information. We immediately notice that human beings are located near the middle.Familiar bodies of atomic matter surround us along an orderly arrangement of points.Since the density of atomic matter has a fairly narrow range, masses increase very nearlyas the cubes of the radii of physical bodies. The mass vs.radius slope in this region of the charts is thus

≈

3, the density vs.radius slope is

≈

0, and since the acceleration dueto gravity varies by the inverse square law, its slope is

≈

1.Moving toward the microcosm along our trail of points, measurements are no longerso straightforward as they are for bulk atomic matter. With sophisticated machinerythe sizes and masses of molecules, atoms, nuclei and particles can be deduced. Thelightest thing whose mass has been reliably measured is an electron. The measurementsare tricky, but at least they yield a deﬁnite result for an electron’s

mass

. The

size

of an electron, on the other hand, is best thought of as more of a theoretical thing thana physical thing. Without going into the reasons for this, suﬃce it to say that, thoughthe two electron radii shown on the graphs are widely recognized as being of theoreticalimportance, it would be erroneous to think of one electron as having such a deﬁnite size.If we include the approximate size of an electron cloud in a ground state hydrogen atom,then these three radii are related to one another by powers of the

ﬁne structure constant

,

α

, and the

Bohr radius

, a

0

.A hydrogen atom without an electron is a proton, whose mass is nearly the same as aneutron. For the purposes of the charts (which take no account of electric

charge

) bothprotons and neutrons are essentially indistinguishible

nucleons

. Muons have the sameelectrical charge as electrons, but are

≈

207 times heavier. Though rare, atoms whoseelectrons are replaced by muons have been created in laboratories. Thus we include

muo-nium

(which lies between the electronic hydrogen atom and the lone proton [nucleon]).With the exception of the lightest elements, nuclei in atoms have nearly the same den-sity, known as

nuclear saturation density

. Thus we ﬁnd another region where the massvs. radius slope

≈

3, the density vs. radius slope

≈

0, and the slope of the accelerationdue to gravity is

≈

1. Note that on these charts the radius and density of one nucleonare derived from the radii and densities actually measured from

collections

of them. Wewill ﬁnd that nuclear saturation density bears a curious relation to atomic density andother key densities when we consider their occurrence in astrophysical phenomena.Which brings us, then, to the opposite direction along our scale of size. In the realmof planets and stars, because of gravity, we get two branches in the pattern: Unlike thecase of smaller bodies of atomic matter where gravity’s role seems negligible, in thisregion, along one branch gravity causes bodies to be more compressed; adding massactually makes the objects get smaller. Along this branch we encounter brown dwarfs,white dwarfs, neutron stars and ﬁnally, extremely compressed stellar objects commonly

Note that the gravitational accelerations corresponding to objectson the Schwarzschild horizon were calculated using

Newton’s

equation. Whereas, according to general relativity, the accelerationof a stationary body at the horizon would be

infinite

. (See, e.g.,Rindler,

Essential Relativity, 2nd Ed

., Springer-Verlag, 1977; p. 149.Or Hartle,

Gravity

, Addison-Wesley, 2003; p. 435.)Also, the

densities

of these objects were calculated as an average—as though the mass were distributed throughout a sphere of radius= 2

GM

/

c

2

. Whereas, according to general relativity, the matter wouldquickly collapse to a central singularity of

infinite

density.An alternative treatment of these extreme and undesirable conse-quences is presented on the otherwise identical graph:

CosmicEverything Chart (SGM).**

This alternative is physically morereasonable—at least insofar as the Post-Newtonian accelerations anddensities are all

finite

; there are

no singularities

. See also

CosmicEverything Charts Compared**

which gives a more thoroughcomparison.**Documents referred to immediately above are accessible atGravitationLab.com or at Scribd.com, under Benish.To minimize clutter, many points are not labeled—especially thosefor acceleration. But everything is labeled at least once. Identi-fication may require finding the point corresponding to a differentquantity along the same vertical line. Moon, Earth, Sun, Milky Wayand Milky Way Core have been colored to facilitate finding theseparticular points.

Fig. 1. – Chart 1. Logarithmic scales of mass, radius, density and gravitational acceleration of objects spanning the range of size of the known universe. Due to the fuzziness of some objects,deviations from spherical shape and uncertainties of measurement, some values are rougherapproximations than others. Being on a logarithmic scale, all quantities shown are neverthelessfairly accurate. This chart is thus a generally reliable representation of key physical magnitudesin our universe, with the possible exception of objects on the Schwarzschild horizon line.